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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 12678–12684
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Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes

Z. Han, V. Van, W. N. Herman, and P.-T. Ho  »View Author Affiliations


Optics Express, Vol. 17, Issue 15, pp. 12678-12684 (2009)
http://dx.doi.org/10.1364/OE.17.012678


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Abstract

We propose and investigate ultracompact aperture-coupled plasmonic ring resonators with submicron bending radii based on strongly-confined metal-insulator-metal plasmonic waveguides. Enhanced coupling can be obtained via diffraction by small apertures having typical widths between 50–100nm in the metallic sidewall between the ring and bus waveguides. Both analytical model and rigorous FDTD simulations show that 500nm-radius ring resonators can be obtained with low insertion loss, wide free spectral range and sub-diffraction cavity volume of less than 0.1(λ0/neff)3.

© 2009 Optical Society of America

1. Introduction

2. Analytical model

Fig. 1(a) shows a schematic of an MIM plasmonic ring resonator with radius R side-coupled to a plasmonic bus waveguide via a small aperture of width w in the ring sidewall. The ring and bus are separated by a gap g, which is also the aperture depth. The ring and bus waveguides consist of a dielectric core layer of thickness d sandwiched between two parallel metallic layers. The waveguides are assumed to support the fundamental TM mode, with propagation length Lp due to absorption loss in the metal. Using Bethe’s small-hole diffraction theory [9

9. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944). [CrossRef]

] and neglecting any plasmon-mediated coupling, we model the small aperture in the ring sidewall by equivalent electric and magnetic dipole moments. These dipoles radiate into the four ports of the coupling junction, giving rise to the forward and backward scattered waves. FDTD simulations of the coupling junctions with various aperture widths and depths showed that the forward coupling and backward coupling differ only slightly, so to simplify our analysis we assume that these couplings are equal, κfr=κ. With reference to Fig. 1(a), the scattering matrix of the four-port aperture coupler can be expressed as

[A1A2A3A4]=[tttt][A1+A2+A3+A4+],
(1)

where t=τ-jκ and for a lossless coupling junction we must have τ2+4κ2=1. Letting A+ 3=0, A3+=0,A2+=A4αrtejϕrt and A4+=A2αrtejϕrt, where ϕrt is the roundtrip phase in the ring and art=exp(-πR/Lp) is the roundtrip amplitude attenuation, we solve (1) for the transmitted response Tt=A - 3/A + 1 and reflected response Tr=A - 1/A + 1 of the device to obtain

Tt=t2κ2αrtejϕrt1ταrtejϕrt,
(2)
Tr=jκ2κ2αrtejϕrt1ταrtejϕrt.
(3)

In Fig. 1(b) we plotted the theoretical response of a plasmonic ring with a 500nm radius for the ideal case of no loss and the practical case where the plasmonic waveguide has a propagation length Lp=50µm, which is typical for MIM waveguides at infrared wavelengths. The aperture power coupling strength is assumed to be κ2=0.1, which, as shown by FDTD simulations below, can be achieved with an aperture width of 50nm. In both cases the reflection response has resonance peaks while the transmission spectrum exhibits resonance dips. The reflection response is also seen to have a highly asymmetric spectral shape with a reflection null near the resonant frequency. This behavior is characteristic of a Fano resonance, which is caused by the interference between the back-scattered wave from the aperture and the discrete resonance modes of the ring cavity. The dip in the reflection spectrum occurs at the frequency where the back-scattered wave and the wave coupled out from the ring interfere destructively with each other. For the lossless device, complete power reflection and zero transmission is obtained at resonance. For the lossy case, even when the propagation length of the ring waveguide is only 50µm (corresponding to an intrinsic Q ~400), the device responses are only slightly degraded, showing a 2dB insertion loss in the reflected signal. Inside the ring, forward and backward scattered waves from the coupling aperture give rise to counter-propagating modes, which interfere to form standing wave patterns at the resonant frequencies. In Fig. 1(b) we also plotted the intensity spectrum inside the lossy ring, which shows that an intensity enhancement near 10dB can be achieved at resonance.

Fig. 1. (a) Schematic of an MIM plasmonic ring resonator side-coupled to a bus waveguide via a small aperture of width w and depth g. (b) Theoretical spectral response of a 500nm-radius plasmonic ring resonator with κ2=0.1 for the ideal lossless case (dashed lines) and the lossy case (solid lines) when the MIM waveguide has a propagation length of 50µm.

3. Numerical results

Fig. 2. (a) Forward κ2 f, blue line) and backward (κ2 f, red line) power coupling coefficients as functions of the aperture width w with fixed aperture depth g=50nm. (b) 2D-FDTD simulation results of the spectral responses of a 500nm-radius plasmonic ring with w=50nm and g=50nm. (c) Time-averaged distribution of the magnetic field, |Hy|2, in the ring at the 1.51µm resonance wavelength. (d) 3D-FDTD simulation results of the spectral responses of a 500nm-radius plasmonic ring resonator with coupling aperture width w=100nm and depth g=50nm. The inset shows the cross-section of the MIM waveguide.

We can also construct aperture-coupled traveling-wave plasmonic ring resonators by using directional aperture couplers in which the back-scattered waves are suppressed. Such a coupler may be realized with two or more identical apertures separated by a length of λ/4. All-pass and four-port add-drop plasmonic ring devices can then be constructed by coupling a metallic ring to one or two MIM waveguides via these multiple-aperture couplers. In Fig. 3(a) we show the theoretical responses of an all-pass and an add-drop plasmonic ring resonator using two-hole directional couplers. The ring radius was 500nm and the waveguides were assumed to have a propagation length of Lp=50µm. To simplify the analysis we have also neglected dispersion in the theoretical model. It is seen that these devices have spectral characteristics that are much like those of conventional dielectric microring resonators. To verify the theoretical responses, we again performed 2D-FDTD simulation of an all-pass plasmonic ring resonator with a 500nm radius coupled to a bus waveguide via a directional coupler consisting of two apertures separated by a distance of 220nm, or approximately λ/4 at the 1.51µm wavelength. The aperture and waveguide dimensions of the device as well as the material parameters were the same as for the device in Fig. 2(b). The transmission and reflection spectral responses of the all-pass plasmonic ring obtained from the simulation are plotted in Fig. 3(b). From the plot it is evident that the reflected signal is suppressed below -11dB at the 1.5µm resonance and the transmitted spectrum has the characteristic dip of a lossy all-pass ring resonator. Due to the extremely dispersive nature of the plasmonic waveguides and the narrow-band nature of the two-hole coupler, suppression of the back-scattered wave could be achieved only around the 1.5µm resonance. However, this is not a concern since the resonator has a very wide FSR so that the adjacent unsuppressed reflection peaks occur 300–400nm away. We also note that better suppression of the back-scattered wave can be achieved by adding more apertures to the coupler. Due to their similar spectral responses as conventional traveling-wave microring resonators, plasmonic ring resonators with directional aperture couplers can be used as basic building blocks to construct more advanced signal processing plasmonic circuits such as filters, multiplexers, switches and delay elements.

Fig. 3. (a) Theoretical spectral responses of an all-pass and an add-drop plasmonic ring resonator using two-hole directional aperture couplers. (b) 2D-FDTD simulation results of the spectral responses of a 500nm-radius all-pass plasmonic ring resonator.

4. Conclusion

Acknowledgments

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

References and links

1.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006). [CrossRef] [PubMed]

2.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855 (1991). [CrossRef]

3.

A. V. Krasavina and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007). [CrossRef]

4.

Rashid Zia, Mark D. Selker, Peter B. Catrysse, and Mark L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442 (2004). [CrossRef]

5.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263 (2004). [CrossRef]

6.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators”, IEEE J. Sel. Topics Quantum Electron. 8, 705 (2002). [CrossRef]

7.

S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express , 14(7), 2932(2006). [CrossRef]

8.

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007). [CrossRef]

9.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944). [CrossRef]

10.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B. 6, 4370–4379 (1972). [CrossRef]

OCIS Codes
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 13, 2009
Revised Manuscript: July 4, 2009
Manuscript Accepted: July 6, 2009
Published: July 10, 2009

Citation
Z. Han, V. Van, W. N. Herman, and P.-T. Ho, "Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes," Opt. Express 17, 12678-12684 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12678


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References

  1. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006). [CrossRef] [PubMed]
  2. F. Yang, J. R. Sambles, and G. W. Bradberry, "Long-range surface modes supported by thin films," Phys. Rev. B 44, 5855 (1991). [CrossRef]
  3. A. V. Krasavina and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phys. Lett. 90, 211101 (2007). [CrossRef]
  4. Rashid Zia, Mark D. Selker, Peter B. Catrysse, and Mark L. Brongersma, "Geometries and materials for subwavelength surface plasmon modes," J. Opt. Soc. Am. A 21, 2442 (2004). [CrossRef]
  5. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263 (2004). [CrossRef]
  6. V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Topics Quantum Electron. 8, 705 (2002). [CrossRef]
  7. S. Xiao, L. Liu and M. Qiu, "Resonator channel drop filters in a plasmon-polaritons metal," Opt. Express,  14(7), 2932(2006). [CrossRef]
  8. A. Hosseini and Y. Massoud, "Nanoscale surface plasmon based resonator using rectangular geometry," Appl. Phys. Lett. 90, 181102 (2007). [CrossRef]
  9. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163 (1944). [CrossRef]
  10. P. Johnson and R. Christy, "Optical constants of the noble metals," Phys. Rev. B. 6, 4370-4379 (1972). [CrossRef]

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